On Vanishing and Cofiniteness of Generalized Local Cohomology Modules

TL;DR

This paper investigates the conditions under which generalized local cohomology modules vanish or are non-zero, explores their relationships with Ext and local cohomology modules, and establishes cofiniteness properties to address existing open questions.

Contribution

It provides new results on vanishing, non-vanishing, and cofiniteness of generalized local cohomology modules, offering alternative insights into their structure and relations.

Findings

Criteria for vanishing and non-vanishing of modules

Relations between generalized local cohomology, Ext, and local cohomology

Cofiniteness properties that answer open questions

Abstract

In this paper, some results on vanishing and non-vanishing of generalized local cohomology modules are presented and some relations between those modules and, Ext and ordinary local cohomology modules are studied. Also, several cofiniteness propositions for generalized local cohomology modules are established which, among other things, provide an alternative answer to a question in [Y2].